JEE Main 2022MathematicsEllipseMediumMCQ

JEE Main 2022 — Ellipse Question with Solution

JEE Main 2022 (25 Jun Shift 2)

Question

The line y=x+1 meets the ellipse x24+y22=1 at two points P and Q. If r is the radius of the circle with PQ as diameter then 3r2 is equal to

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Show full solutionCorrect option: A
Correct answer
A20

Step-by-step explanation

Plotting the diagram of given data we have,

Let P be the point -1+p2,p2

Since it lies on the ellipse x24+y22=1, we get 

-1+p224+p222=1 ⇒3p28-p22-34=0

Here p1-p22=2232-4-2=89+8=809

We know, p1-p22=PQ2

⇒ PQ2=809

Now r=PQ2⇒9r2=9PQ24=94×809=20

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About this question

This is a previous-year question from JEE Main 2022, covering the Ellipse chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.